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Enter command mode: high on KEY pinout. Very important to set communication speed to 38400bps because command mode talks in this speed, BUT Arduino to the serial monitor MUST still on 9600bps

set up based on this article

For some reason, this Bluetooth module (A) can't be worked well for me. The pair was a success, but the link always failed.

So I switched this version of Bluetooth (B) HC-05 module:

It has a small button to enter AT mode. In AT mode it needs just a next few commands:
AT+PSWD=1234 # set up the right password
AT+INIT
AT+PAIR=12,34,56789c72,20 (,20 means 20 second timeout)
AT+BIND=12,34,56789c72
AT+LINK=12,34,56789c72
note: capital letters must be used!!! After switched back from AT mode, and typed ATI command, the ELM was answered to me, so the first trial was successful!

I used this connection for both

Address: 0x27

used library: LiquidCrystal I2C by Frank de Brabander version 1.1.2